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/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
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 */

package org.apache.commons.math3.ode.nonstiff;

import org.apache.commons.math3.ode.sampling.StepInterpolator;

/**
 * This class implements a step interpolator for the classical fourth
 * order Runge-Kutta integrator.
 *
 * 

This interpolator allows to compute dense output inside the last * step computed. The interpolation equation is consistent with the * integration scheme : *

    *
  • Using reference point at step start:
    * y(tn + θ h) = y (tn) * + θ (h/6) [ (6 - 9 θ + 4 θ2) y'1 * + ( 6 θ - 4 θ2) (y'2 + y'3) * + ( -3 θ + 4 θ2) y'4 * ] *
  • *
  • Using reference point at step end:
    * y(tn + θ h) = y (tn + h) * + (1 - θ) (h/6) [ (-4 θ^2 + 5 θ - 1) y'1 * +(4 θ^2 - 2 θ - 2) (y'2 + y'3) * -(4 θ^2 + θ + 1) y'4 * ] *
  • *
*

* * where θ belongs to [0 ; 1] and where y'1 to y'4 are the four * evaluations of the derivatives already computed during the * step.

* * @see ClassicalRungeKuttaIntegrator * @since 1.2 */ class ClassicalRungeKuttaStepInterpolator extends RungeKuttaStepInterpolator { /** Serializable version identifier. */ private static final long serialVersionUID = 20111120L; /** Simple constructor. * This constructor builds an instance that is not usable yet, the * {@link RungeKuttaStepInterpolator#reinitialize} method should be * called before using the instance in order to initialize the * internal arrays. This constructor is used only in order to delay * the initialization in some cases. The {@link RungeKuttaIntegrator} * class uses the prototyping design pattern to create the step * interpolators by cloning an uninitialized model and latter initializing * the copy. */ // CHECKSTYLE: stop RedundantModifier // the public modifier here is needed for serialization public ClassicalRungeKuttaStepInterpolator() { } // CHECKSTYLE: resume RedundantModifier /** Copy constructor. * @param interpolator interpolator to copy from. The copy is a deep * copy: its arrays are separated from the original arrays of the * instance */ ClassicalRungeKuttaStepInterpolator(final ClassicalRungeKuttaStepInterpolator interpolator) { super(interpolator); } /** {@inheritDoc} */ @Override protected StepInterpolator doCopy() { return new ClassicalRungeKuttaStepInterpolator(this); } /** {@inheritDoc} */ @Override protected void computeInterpolatedStateAndDerivatives(final double theta, final double oneMinusThetaH) { final double oneMinusTheta = 1 - theta; final double oneMinus2Theta = 1 - 2 * theta; final double coeffDot1 = oneMinusTheta * oneMinus2Theta; final double coeffDot23 = 2 * theta * oneMinusTheta; final double coeffDot4 = -theta * oneMinus2Theta; if ((previousState != null) && (theta <= 0.5)) { final double fourTheta2 = 4 * theta * theta; final double s = theta * h / 6.0; final double coeff1 = s * ( 6 - 9 * theta + fourTheta2); final double coeff23 = s * ( 6 * theta - fourTheta2); final double coeff4 = s * (-3 * theta + fourTheta2); for (int i = 0; i < interpolatedState.length; ++i) { final double yDot1 = yDotK[0][i]; final double yDot23 = yDotK[1][i] + yDotK[2][i]; final double yDot4 = yDotK[3][i]; interpolatedState[i] = previousState[i] + coeff1 * yDot1 + coeff23 * yDot23 + coeff4 * yDot4; interpolatedDerivatives[i] = coeffDot1 * yDot1 + coeffDot23 * yDot23 + coeffDot4 * yDot4; } } else { final double fourTheta = 4 * theta; final double s = oneMinusThetaH / 6.0; final double coeff1 = s * ((-fourTheta + 5) * theta - 1); final double coeff23 = s * (( fourTheta - 2) * theta - 2); final double coeff4 = s * ((-fourTheta - 1) * theta - 1); for (int i = 0; i < interpolatedState.length; ++i) { final double yDot1 = yDotK[0][i]; final double yDot23 = yDotK[1][i] + yDotK[2][i]; final double yDot4 = yDotK[3][i]; interpolatedState[i] = currentState[i] + coeff1 * yDot1 + coeff23 * yDot23 + coeff4 * yDot4; interpolatedDerivatives[i] = coeffDot1 * yDot1 + coeffDot23 * yDot23 + coeffDot4 * yDot4; } } } }




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